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Value at risk et expected shortfall pour des données faiblement dépendantes : estimations non-paramétriques et théorèmes de convergences

Abstract : To quantify and measure the risk in an environment partially or completely uncertain is probably one of the major issues of the applied research in financial mathematics. That relates to the economy, finance, but many other fields like health via the insurances for example. One of the fundamental difficulties of this process of management of risks is to model the under lying credits, then approach the risk from observations or simulations. As in this field, the risk or uncertainty plays a fundamental role in the evolution of the credits; the recourse to the stochastic processes and with the statistical methods becomes crucial. In practice the parametric approach is largely used.It consists in choosing the model in a parametric family, to quantify the risk according to the parameters, and to estimate its risk by replacing the parameters by their estimates. This approach presents a main risk, that badly to specify the model, and thus to underestimate or over-estimate the risk. Based within and with a view to minimizing the risk model, we choose to tackle the question of the quantification of the risk with a nonparametric approach which applies to models as general as possible. We concentrate to two measures of risk largely used in practice and which are sometimes imposed by the national or international regulations. They are the Value at Risk (VaR) which quantifies the maximum level of loss with a high degree of confidence (95% or 99%). The second measure is the Expected Shortfall (ES) which informs about the average loss beyond the VaR.
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Ali Kabui. Value at risk et expected shortfall pour des données faiblement dépendantes : estimations non-paramétriques et théorèmes de convergences. Mathématiques générales [math.GM]. Université du Maine, 2012. Français. ⟨NNT : 2012LEMA1008⟩. ⟨tel-00743159⟩

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